A130722 The twice repeated nonnegative integers at even indices, the non-repeated nonnegative integers at odd indices.

0, 0, 0, 1, 1, 2, 1, 3, 2, 4, 2, 5, 3, 6, 3, 7, 4, 8, 4, 9, 5, 10, 5, 11, 6, 12, 6, 13, 7, 14, 7, 15, 8, 16, 8, 17, 9, 18, 9, 19, 10, 20, 10, 21, 11, 22, 11, 23, 12, 24, 12, 25, 13, 26, 13, 27, 14, 28, 14, 29, 15, 30, 15, 31, 16, 32, 16, 33, 17, 34, 17, 35, 18, 36, 18, 37, 19, 38, 19, 39

Offset: 0

Author

Paul Curtz, Aug 16 2007

Keywords

• nonn
• easy

Crossrefs

Cf. A001477, A004526, A005044.

Programs

Maple

a := n -> A005044(n+2) - A005044(n-7): A005044 := n -> floor((1/48)*(n^2 + 3*n + 21 + (-1)^(n-1)*3*n)): seq(a(n), n=0..79); # Johannes W. Meijer, Oct 08 2013

Mathematica

Table[Sum[Sign[Mod[n - 2 i, 4]], {i, Floor[n/2]}], {n, 0, 100}] (* Wesley Ivan Hurt, Apr 10 2018 *)

PARI

a(n) = if(n%2, n\2, n\4); \\ Altug Alkan, Apr 16 2018

Formula

a(2*n) = A004526(n) = floor(n/2). a(2*n+1) = A001477(n) = n.

O.g.f.: (x^2+x+1)*x^3/((x-1)^2*(1+x)^2*(1+x^2)). - R. J. Mathar, Jul 07 2008

a(n) = A005044(n+2) - A005044(n-7). - Johannes W. Meijer, Oct 08 2013

a(n) = Sum_{i=1..floor(n/2)} sign((n-2i) mod 4). - Wesley Ivan Hurt, Apr 10 2018

a(n) = A106466(n-3) for n>=3. - Georg Fischer, Oct 07 2018

Extensions

Edited by R. J. Mathar, Jul 07 2008